Random Contractions in Global Risk Governance

Series Editor’s Foreword
Preface
Contents
1 Stochastic Concepts in Global Risk Governance Operations
	1.1 Introduction
	1.2 Structural Aspects of Global Risks
	1.3 Concepts of Global Risk Governance and Probability Theory
	1.4 Information Dimensions of Global Risk Governance
	1.5 Conclusions
	References
2 Consideration in Modeling of Random Contractions
	2.1 Introduction
	2.2 Defining Random Contractions
	2.3 Distribution Function of a Random Contraction
	2.4 Probability Density Function of a Random Contraction
	2.5 Characteristic Function of a Random Contraction
	2.6 Several Fundamental Classes of Random Contractions
	2.7 Class of a-Unimodal Random Contractions
	2.8 Class of v-Unimodal Random Contractions
	2.9 Class of Random Contractions of Maxima of Random Number of Random Variables
	2.10 Class of Random Contractions of Minima of Random Number of Random Variables
	2.11 Class of Random Contractions of Present Value Stochastic Integrals
	2.12 Class of Random Contractions of Random Sums
	2.13 Class of Random Contractions of Present Values
	2.14 Class of Random Contractions of Bernoulli Selections
	2.15 Conclusions
	References
3 Formulations and Investigations of Random Contractions
	3.1 Introduction
	3.2 Formulation of a Stochastic Multiplicative Model
	3.3 Representation as a Random Contraction of a Stochastic Multiplicative Model
	3.4 Extending the Contraction of a Random Sum
	3.5 Interpretation of the Formulated Random Contraction in Stochastic Discounting
	3.6 Characteristic Function of the Formulated Stochastic Discounting Model
	3.7 Extension of a Stochastic Multiplicative Model
	3.8 Representation as a Random Contraction of an Extension of a Stochastic Multiplicative Model
	3.9 Characteristic Function of an Extension of a Random Contraction
	3.10 Characterizing an Extension of a Random Contraction
	3.11 Representation of an Extension of a Random Contraction as a Stochastic Discounting Model
	3.12 Characteristic Function of the Representation as a Stochastic Discounting Model of an Extension of a Random Contraction
	3.13 Characterizing the Representation as a Stochastic Discounting Model of an Extension of a Random Contraction
	3.14 Conclusions
	References
4 Interpretations of Random Contractions in Global Risk Governance
	4.1 Introduction
	4.2 Number of Impaired Systems
	4.3 Global Risk Severity
	4.4 Discounted Global Risk Severity
	4.5 Global Risk Severity Reduction
	4.6 Global or Regional Risk Severity
	4.7 Discounted Global or Regional Risk Severity
	4.8 Global or Regional Risk Severity Reduction
	4.9 Practical Research Purposes
	4.10 Model of Impaired Systems Number
	4.11 Model of Global Risk Severity
	4.12 Model of Discounted Global Risk Severity
	4.13 Model of Global Risk Severity Reduction
	4.14 Model of Global or Regional Risk
	4.15 Model of Discounted Global or Regional Risk Severity
	4.16 Model of Global or Regional Risk Severity Reduction
	4.17 Conclusions
	References